Let f(x) = (bx+c)^2-{(a^2)(x^4)}
f(0) = (b0+c)^2-{(a^2)(0^4)} = c2
now we know f(0) is positive
f(-c/b) = (b(-c/b)+c)^2-{(a^2)((-c/b)^4)} = – {(a^2)((-c/b)^4)}
So f(-c/b) is negative.
since f is polynomial it is always continous and it changes sogn from + to – hence by IVT it must have root between -c/b and 0.
also degree of f id 4 and nonn real roo occur in pairs hence 1 real root imply another real root
